Time Allocations, Social Norms, and Gender Gaps

Kazuharu Yanagimoto

December 16, 2022

Female Workers in Japan


Gap in Median Earnings of Full-time Workers in 2019

Fraction of Part-time in Female Workers in 2019

Female Laborforce Participation in 2019

  • Large gap in earnings and high ratio of part-time jobs
  • Female participation is not low

Why is the gender wage gap large in Japan?

Why is the fraction of part-time workers large for women in Japan?

What Do I Do?

Document Female Employment in Japan

  • Large gender diff. in participation, occupations, working hours, and wage
  • Regular vs Non-regular job
  • Social norms on gender roles

Build a model

Choices on occupations and working hours

  • Household members can choose not to work
  • Occupations differ in the way hours map into earnings (linear vs. convex)

Utility cost associated to social norms

  • Wives earnings more than husbands

Model explains

  • All gender gaps in participation
  • 33% in occupational choices, 74% in labor hours, and 34% in wage

Related Literature↗

Facts

Data

Japan Panel Study of Employment Dynamics (JPSED)

  • 57,284 men and women older than 15 in Japan
  • Panel data 2015-2019
  • Earnings, working hours, housework, labor contracts (main earner and spouse)
  • Use samples aged 25-59

Survey on Dual-Income Couples’ Household Economy and Attitudes

  • 2200 couples, aged 35-49 (30-55) for females (males), in the Greater Tokyo Area
  • One-year survey in 2014
  • Earnings, working hours, housework, types of contracts

Regular and Non-regular Jobs

In Japanese statistics, a definition is used: Regular and Non-regular Jobs

  • Based on “how their occupations are classified in the company”
  • There is no precise definition

However, they are typically

Regular Non-Regular
Contract Permanent Temporary
Hours (week) 40/40+ Lower and Dispersed
Wage High Low

In JPSED,

  • 92 % (91 %) of male (female) regular workers have permanent contracts
  • 13 % (14 %) of male (female) non-regular workers have permanent contracts

Distribution of Weekly Working Hours

Distribution of Hourly Wage (1K JPY ≈ 6.9 EUR)

Occupational Choices of Married Men and Women

Why Do Women Choose Non-regular Jobs?


Flexibility of the Job

Reasons for Choosing Non-regular Job, Women

Job Flexibility and Convex Earning


Goldin (2014) defines the two types of jobs by earning schedule

  • Linear jobs are lower wages and high flexibility
  • Non-linear (convex) jobs are high wage and low flexibility

These characteristics correspond to Regular and Non-regular jobs!
Regression↗

Social Norms


Bertrand, Kamenica, and Pan (2015)

  • a gap in the density of wife’s share of earnings in couples at 50% in US
  • interpreted as the existence of social norms


Japanese Data

  • stark gap is seen in Japanese data
  • rising pattern just before 50%

Marriage Penalty

If there are social norms regarding wives earning more than husbands, after the marriage, women might choose:

  • lower working hours
  • changing/quitting jobs


Using JPSED2016-2020, I see

  • Men and Women married at 2018
  • Change in market outcomes in 2017
  • Child Penalty as in Kleven, Landais, and Søgaard (2019)

Yearly Earnings (JPY)

Female earnings decline by 4496 EUR 1-year after the marriage
Other Outcomes↗

Key Features

  1. Regular vs. Non-regular
  2. Social norms on wife’s earnings

Four Key Gender Gaps

Sample: married, 25-59 aged in JPSED2016-2020

1. Participation Rate (0.27)

98 % (male) - 70 % (female)

2. Occupational Choices (0.59)

Fraction of regular workers. 89 % (male) - 32 % (female)

3. Labor Hours (0.49)

Mean of log working hours. 44.2 hours (male), 20.3 hours (female) per week

4. Wage (0.76)

Mean of log wage. 2958 JPY (male), 1534 JPY (female)

Model

Households’ Problem

  • Economy consists of couples, including husbands \((g = m)\) and wives \((g = f)\)
  • choose an occupation \(j_g\) from regular \(R\), non-regular \(NR\), not-working \(NW\)
  • Endowed one unit of time, and choose working hours \(h_m, h_f\), home hours \(T_m, T_f\), and leisure \(1 - h_m - T_m, 1 - h_f - T_f\)

\[ \max_{h_m, h_f, T_m, T_f, j_m, j_f} U = \log c + \gamma \log H(1 - h_m - T_m, 1 - h_f - T_f) - \delta I\{e_m < e_f\} \]

subject to

\[\begin{aligned} c &= e(h_m, j_m) + e(h_f, j_f) \\ T &= T_m + T_f \end{aligned} \]

\(H(\cdot)\) : Joint leisure function
\(e(h, j)\) : Earning
\(T\) : Home hours requirement
\(\delta\) : Utility cost

Productivity

Each husband and wife is endowed job specific productivity:

\[ \begin{pmatrix}a_{m, R} \\ a_{f, R} \\ a_{m, NR} \\ a_{f, NR}\end{pmatrix} \sim \log\mathcal{N}\left(\begin{pmatrix}0 \\ 0 \\ \mu_{NR} \\ \mu_{NR}\end{pmatrix}, \begin{pmatrix} \sigma^2 & \rho_{mf}\sigma^2 & \rho_{R, NR}\sigma^2 & \rho_{R, NR}\rho_{mf} \sigma^2 \\ \cdot & \sigma^2 & \rho_{R, NR}\rho_{mf} \sigma^2 & \rho_{R, NR} \sigma^2 \\ \cdot & \cdot & \sigma^2 & \rho_{mf} \sigma^2 \\ \cdot & \cdot & \cdot & \sigma^2 \end{pmatrix}\right) \]

\(\mu_{NR} < 0 \Rightarrow\) Non-regular workers earns less than regular worker

\(\rho_{mf} > 0 \Rightarrow\) Assortative Mating

\(\rho_{R, NR} > 0 \Rightarrow\) Regular and Non-regular abilities are linked


No Gender Difference in Productivity

Convex Wage Schedules


Regular Jobs

\[ e(h, R) = \begin{cases} a_R h^{1 + \theta} & h < \bar{h} \\ a_R \left(\bar{h}^{1 + \theta} + \lambda_{R} \bar{h}^{\theta}(h - \bar{h})\right) & h > \bar{h} \end{cases} \]


Non-regular Jobs

\[ e(h, NR) = \begin{cases} a_{NR} h & h \le \bar{h} \\ a_{NR} \left(\bar{h} + \lambda_{NR} (h - \bar{h})\right) & h > \bar{h} \end{cases} \]

Leisure Function

\[ H = \left(\nu(1 - h_m - T_m)^{\xi} + (1 - \nu)(1 - h_f - T_f)^{\xi}\right)^{1/\xi} \]

\(\nu\) : share parameter. Each household is endowed \(\nu \sim Beta(\alpha_{\nu}, \beta_{\nu})\)
\(\xi\) : complementarity. \(\xi < 0 \Rightarrow\) complement

Home Hours Requirement

\[ \begin{aligned} T &= T_m + T_f \\ \frac{1}{2}T & \sim Beta(\alpha_T, \beta_T) \end{aligned} \]

  • Households has a home hours requirement \(T \in [0, 2]\)
  • \(T\) does not increase the utility
  • captures the heterogeneity of home hours requirements (children)

Estimation

Calibration Strategy


15 Parameters

\[ \{\underbrace{\lambda_{R}, \lambda_{NR},\theta, }_{\text{production function}} \underbrace{\mu_{NR}, \sigma^2, \rho_{R, NR}, \rho_{mf},}_{\text{productivity}} \,\, \underbrace{\gamma, \xi, \alpha_{\nu}, \beta_{\nu},}_{\text{leisure}} \underbrace{\alpha_{T}, \beta_{T},}_{\text{home hours }} \underbrace{\alpha_{\delta}, \beta_{\delta}}_{\text{social norm}}\} \]


Method of Simulated Moments

  1. Model produces occupations, working hours, and wages of household
  2. Compute 15 moments (e.g. ratio of regular workers, mean of working hours, gender correlation of wage…)
  3. Minimize the distance between moments from data and model

Estimation

Parmeter Value Target Data Model

λR

0.57

mean of hf for regular workers

0.50 0.48

λNR

0.63

mean of hf for NR workers

0.30 0.27

θ

2.96

share of regular workers, females

0.32 0.37

μNR

−3.15

share of NR workers, females

0.38 0.28

σ

1.03

s.d. of ln wf) for R workers

0.72 0.72

ρR, NR

0.14

mean diff. of ln wf, R and ln wf, NR

0.62 0.62

ρmf

0.01

corr. of log wages, R×R couples

0.49 0.50

γ

0.84

s.d. of hf for regular workers

0.11 0.11

ξ

−8.29

s.d. of hf for NR workers

0.14 0.15

αν

13.04

mean of Tm for regular workers

0.14 0.13

βν

1.15

mean of Tm for NR workers

0.13 0.14

αT

1.59

mean of Tf for regular workers

0.28 0.21

βT

3.57

mean of Tf for NR workers

0.32 0.37

αδ

0.59

share of couples with em < ef

0.07 0.08

βδ

11.81

corr. of working hours, couples

0.19 0.18

Estimation

Parmeter Value Target Data Model

λR

0.57

mean of hf for regular workers

0.50 0.48

λNR

0.63

mean of hf for NR workers

0.30 0.27

θ

2.96

share of regular workers, females

0.32 0.37

μNR

−3.15

share of NR workers, females

0.38 0.28

σ

1.03

s.d. of ln wf) for R workers

0.72 0.72

ρR, NR

0.14

mean diff. of ln wf, R and ln wf, NR

0.62 0.62

ρmf

0.01

corr. of log wages, R×R couples

0.49 0.50

γ

0.84

s.d. of hf for regular workers

0.11 0.11

ξ

−8.29

s.d. of hf for NR workers

0.14 0.15

αν

13.04

mean of Tm for regular workers

0.14 0.13

βν

1.15

mean of Tm for NR workers

0.13 0.14

αT

1.59

mean of Tf for regular workers

0.28 0.21

βT

3.57

mean of Tf for NR workers

0.32 0.37

αδ

0.59

share of couples with em < ef

0.07 0.08

βδ

11.81

corr. of working hours, couples

0.19 0.18

\(\xi < 0\)

  • Leisure by husband and wife is complement

Estimation

Parmeter Value Target Data Model

λR

0.57

mean of hf for regular workers

0.50 0.48

λNR

0.63

mean of hf for NR workers

0.30 0.27

θ

2.96

share of regular workers, females

0.32 0.37

μNR

−3.15

share of NR workers, females

0.38 0.28

σ

1.03

s.d. of ln wf) for R workers

0.72 0.72

ρR, NR

0.14

mean diff. of ln wf, R and ln wf, NR

0.62 0.62

ρmf

0.01

corr. of log wages, R×R couples

0.49 0.50

γ

0.84

s.d. of hf for regular workers

0.11 0.11

ξ

−8.29

s.d. of hf for NR workers

0.14 0.15

αν

13.04

mean of Tm for regular workers

0.14 0.13

βν

1.15

mean of Tm for NR workers

0.13 0.14

αT

1.59

mean of Tf for regular workers

0.28 0.21

βT

3.57

mean of Tf for NR workers

0.32 0.37

αδ

0.59

share of couples with em < ef

0.07 0.08

βδ

11.81

corr. of working hours, couples

0.19 0.18

\(\xi < 0\)

  • Leisure by husband and wife is complement

\(\alpha_{\nu} =\) 13.04, \(\beta_{\nu} =\) 1.15

  • \(E[\nu] =\) 0.92 > 0.5
  • Husbands have a higher weight on joint leisure

Estimation

Parmeter Value Target Data Model

λR

0.57

mean of hf for regular workers

0.50 0.48

λNR

0.63

mean of hf for NR workers

0.30 0.27

θ

2.96

share of regular workers, females

0.32 0.37

μNR

−3.15

share of NR workers, females

0.38 0.28

σ

1.03

s.d. of ln wf) for R workers

0.72 0.72

ρR, NR

0.14

mean diff. of ln wf, R and ln wf, NR

0.62 0.62

ρmf

0.01

corr. of log wages, R×R couples

0.49 0.50

γ

0.84

s.d. of hf for regular workers

0.11 0.11

ξ

−8.29

s.d. of hf for NR workers

0.14 0.15

αν

13.04

mean of Tm for regular workers

0.14 0.13

βν

1.15

mean of Tm for NR workers

0.13 0.14

αT

1.59

mean of Tf for regular workers

0.28 0.21

βT

3.57

mean of Tf for NR workers

0.32 0.37

αδ

0.59

share of couples with em < ef

0.07 0.08

βδ

11.81

corr. of working hours, couples

0.19 0.18

\(\xi < 0\)

  • Leisure by husband and wife is complement

\(\alpha_{\nu} =\) 13.04, \(\beta_{\nu} =\) 1.15

  • \(E[\nu] =\) 0.92 > 0.5
  • Husbands have a higher weight on joint leisure

\(\alpha_{T} =\) 1.59, \(\beta_{T} =\) 3.57

  • Home hours requirement is 49 hours per week

Occupational Choices (Not-Targeted)

Time Allocations (Not-Targeted)

Hours Worked

Home Hours

Social Norms


Gender Gaps


Data Model Model / Data Pct.
Participation 0.27 0.27
99%
Occupation 0.59 0.19
33%
Labor Hours 0.49 0.36
74%
Wage 0.76 0.26
34%


Gender Gaps


Data Model Model / Data Pct.
Participation 0.27 0.27
99%
Occupation 0.59 0.19
33%
Labor Hours 0.49 0.36
74%
Wage 0.76 0.26
34%


Model explains

  • Almost all the gap in the participation rate

Gender Gaps


Data Model Model / Data Pct.
Participation 0.27 0.27
99%
Occupation 0.59 0.19
33%
Labor Hours 0.49 0.36
74%
Wage 0.76 0.26
34%


Model explains

  • Almost all the gap in the participation rate
  • Significant proportion of other gender gaps

Mechanism

Why Are the Gaps Large in Japan?


1. Inflexibility of Regular Job \(\theta\)

Given a large amount of housework, women might not choose regular jobs


2. Social Norms \(\delta\)

Social norms might lead wives to work less or not


To verify these arguments, I conduct experiments of \(\theta = 0\) and \(\delta = 0\)

Flexible Regular Job: Occupational Choices


Eliminating inflexibility encourages wives to have regular jobs

No Social Norm: Occupational Choices

No social norms

\(\Rightarrow\) More wives choose regular job

\(\Rightarrow\) More husbands choose not to work

Mechanism

Baseline θ = 0.0 δ = 0.0 Gap θ Gap δ
Participation 0.27 0.14 −0.04
Occupation 0.19 0.01 0.18
Labor Hours 0.36 0.64 0.17
Wage 0.26 −0.03 0.22

Mechanism

Baseline θ = 0.0 δ = 0.0 Gap θ Gap δ
Participation 0.27 0.14 −0.04
Occupation 0.19 0.01 0.18
Labor Hours 0.36 0.64 0.17
Wage 0.26 −0.03 0.22


Job inflexibility \(\theta\)

  • The main element prevents women from having regular jobs
  • Wage gap comes from occupational differences

Mechanism

Baseline θ = 0.0 δ = 0.0 Gap θ Gap δ
Participation 0.27 0.14 −0.04
Occupation 0.19 0.01 0.18
Labor Hours 0.36 0.64 0.17
Wage 0.26 −0.03 0.22


Job inflexibility \(\theta\)

  • The main element that prevents women from having regular jobs
  • Wage gap comes from occupational differences

Social Norms \(\delta\)

  • Explains intensive and extensive margin of male and female participation

Conclusion

Build a Model

  • Regular (inflexible, high wage) vs. Non-Regular (flexible, low wage)
  • Social Norms (wives’ higher earnings)

Model Explains the Gender Gaps

  • Almost all of participation rate
  • 33% in occupational choices, 74% in labor hours, and 34% in wage

Mechanism

  • Job flexibility and social norm play an important role in gender gaps
  • Housework services could reduce the gaps under job inflexibility and social norm (Appendix↗)

Outsourcing of Housework

Outsourcing of Housework


Outsourcing housework could increase women’s labor supply

Raz-Yurovich and Marx (2019), Halldén and Stenberg (2014)


Also discussed as the impact of low-skilled immigrants

Cortés and Tessada (2011), Barone and Mocetti (2011), Farré, González, and Ortega (2011)


However, those housework services are rarely used in Japan

  • Japan has a restrictive policy on immigration
  • 2+ member households pay 7.3 EUR per YEAR on average

Baseline Model with Housework Service

\[\max_{h_m, h_f, j_m, j_f} U = \log c + \gamma \log H - \delta \mathbb{1}(e_m < e_f)\]

subject to

\[ \begin{aligned} c + pt &= e(h_m, j_m) + e(h_f, j_f)\\ H &= (\nu(1 - h_m - T_m)^\xi + (1 - \nu)(1 - h_f - T_f)^\xi)^{1/\xi} \\ T &= T_m + T_f + t \end{aligned} \]

\(t\): housework service
\(p\): price of housework service

Experiment:

  • Fix parameters in the baseline model
  • Set price as the median wage of non-regular job \((p = \exp(\mu_{a_{NR}}))\)

Outsourcing \(T\): Home Hours


Workers use outside services to do most of the home work

Outsourcing \(T\): Gender Gaps


Base Outsourcing t Gap remained Pct.
Participation 0.27 −0.02
−7%
Occupation 0.19 0.03
15%
Labor Hours 0.36 0.06
17%
Wage 0.26 0.25
97%


Given social norms, housework services

Outsourcing \(T\): Gender Gaps


Base Outsourcing t Gap remained Pct.
Participation 0.27 −0.02
−7%
Occupation 0.19 0.03
15%
Labor Hours 0.36 0.06
17%
Wage 0.26 0.25
97%


Given social norms, housework services

  • Reduce gender gaps in participation, occ. choices, and labor hours

Outsourcing \(T\): Gender Gaps


Base Outsourcing t Gap remained Pct.
Participation 0.27 −0.02
−7%
Occupation 0.19 0.03
15%
Labor Hours 0.36 0.06
17%
Wage 0.26 0.25
97%


Given social norms, housework services

  • Reduce gender gaps in participation, occupational choices, and labor hours
  • Do not reduce wage gap

Slide↩︎

Appendix

Related Literature

Home Hours and Gender Gaps

Erosa et al. (2022)

  • Models couples’ decisions on occupations with different job flexibility

Cubas, Juhn, and Silos (2019)

  • Women are penalized for the lack of work in the peak hours (8am-5pm)

Social Norms and Occupational Choices

Bertrand, Kamenica, and Pan (2015)

  • A sharp gap in the wife’s earnings relative to the husband’s earnings

Gender Gaps in Japan

Kitao and Mikoshiba (2022)

  • Role of fiscal policies on female labor force participation and occ. choices

Job Flexibility and Convex Earning

To see the convex and linear wage schedules, similar to
Bick, Blandin, and Rogerson (2022),


\[y_{it} = a_{i} + \lambda_t + \left(\sum_{h \in H, h \ne 40} \beta_h I_{ith}\right) + \gamma X_{it} + \varepsilon_{it}\]


\(y_{it}\) : yearly earnings of individual \(i\) at time \(t\)
\(a_{i}\) : individual fixed effect
\(\lambda_{t}\) : time fixed effect
\(X_{it}\) : age, age-square, educational attainment, industry
\(H = \{20\mbox{-}24, 25\mbox{-}29, \dots, 60\mbox{-}64\}\) : 5 hour bins for weekly working hours
\(I_{ith}\) : indicator if \(i\)’s working hours in the bin \(h \in H\) at time \(t\)

Earning Curves

Regular Jobs

  • Convexity before 40 hours
    \(\Rightarrow\) Concentration at 40 hours
  • After 40 hours, the slope is different from the below-40-hour

Non-regular Jobs

  • Almost linear relationship

Slide↩︎

Marriage Penalty

Participation Rate

Ratio of Regular Workers

Weekly Working Hours

Hourly Wage (JPY)

Slide↩︎

References

Barone, Guglielmo, and Sauro Mocetti. 2011. “With a Little Help from Abroad: The Effect of Low-Skilled Immigration on the Female Labour Supply.” Labour Economics 18 (5): 664–75. https://doi.org/10.1016/j.labeco.2011.01.010.
Bertrand, Marianne, Emir Kamenica, and Jessica Pan. 2015. “Gender Identity and Relative Income Within Households *.” The Quarterly Journal of Economics 130 (2): 571–614. https://doi.org/10.1093/qje/qjv001.
Bick, Alexander, Adam Blandin, and Richard Rogerson. 2022. “Hours and Wages*.” The Quarterly Journal of Economics, January, qjac005. https://doi.org/10.1093/qje/qjac005.
Cortés, Patricia, and José Tessada. 2011. “Low-Skilled Immigration and the Labor Supply of Highly Skilled Women.” American Economic Journal: Applied Economics 3 (3): 88–123. https://www.jstor.org/stable/41288640.
Cubas, German, Chinhui Juhn, and Pedro Silos. 2019. “Coordinated Work Schedules and the Gender Wage Gap,” December, w26548. https://doi.org/10.3386/w26548.
Erosa, Andrés, Luisa Fuster, Gueorgui Kambourov, and Richard Rogerson. 2022. “Hours, Occupations, and Gender Differences in Labor Market Outcomes.” American Economic Journal: Macroeconomics 14 (3): 543–90. https://doi.org/10.1257/mac.20200318.
Farré, Lidia, Libertad González, and Francesc Ortega. 2011. “Immigration, Family Responsibilities and the Labor Supply of Skilled Native Women.” The B.E. Journal of Economic Analysis & Policy 11 (1). https://doi.org/10.2202/1935-1682.2875.
Goldin, Claudia. 2014. “A Grand Gender Convergence: Its Last Chapter.” American Economic Review 104 (4): 1091–1119. https://doi.org/10.1257/aer.104.4.1091.
Halldén, Karin, and Anders Stenberg. 2014. “The Relationship Between Hours of Domestic Services and Female Earnings: Panel Register Data Evidence from a Reform.” SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2534703.
Kitao, Sagiri, and Minamo Mikoshiba. 2022. “Why Women Work the Way They Do in Japan: Roles of Fiscal Policies.” SSRN Electronic Journal. https://doi.org/10.2139/ssrn.4054049.
Kleven, Henrik, Camille Landais, and Jakob Egholt Søgaard. 2019. “Children and Gender Inequality: Evidence from Denmark.” American Economic Journal: Applied Economics 11 (4): 181–209. https://doi.org/10.1257/app.20180010.
Raz-Yurovich, Liat, and Ive Marx. 2019. “Outsourcing Housework and Highly Skilled Women’s Labour Force ParticipationAn Analysis of a Policy Intervention.” European Sociological Review 35 (2): 205–24. https://doi.org/10.1093/esr/jcz001.